Energy Loss Effect in High Energy nuclear Drell-Yan Process

Transcription

1 Energy Loss Effect in High Energy nuclear Drell-Yan Process arxiv:hep-ph/ v1 13 May 2004 ChunGui Duan 1,5 LiHua Song 1 LiJuan Huo 2 GuangLie Li 3,4,5 1.Department of Physics, Hebei Normal University, ShijiaZhuang,050016,China 2.physics department, Shijiazhuang Vocational and Technical institute,shijiazhuang,050081,china 3.Institute of High Energy Physics,CAS,Beijing ,China. 4.Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Acceleration of Lanzhou,Lanzhou,730000,China. 5.CCAST (World Laboratory).P.O.Box8730,Beijing ,China Abstract The energy loss effect in nuclear matter,which is another nuclear effect apart from the nuclear effect on the parton distribution as in deep inelastic scattering process,can be measured best by the nuclear dependence of the high energy nuclear Drell-Yan process. By means of the nuclear parton distribution studied only with lepton deep inelastic scattering experimental data, measured Drell-Yan production cross sections for 800GeV proton incident on a variety of nuclear targets are analyzed within Glauber framework which takes into account energy loss of the beam proton. It is shown that the theoretical results with considering the energy loss effect are in good agreement with the FNAL E866. Keywords: Drell-Yan,energy loss,multiple scattering PACS:11.80.La,13.85.QK, h I Introduction Propagating of a high energy particle through a nuclear medium is of interest in many areas of physics. High energy proton-nucleus scattering has been studied for many decades by both the nuclear and particle physics communities [1]. By means of the nuclei, we can study the space-time development of the strong 1

2 interaction during its early stages, which is inaccessible between individual hadrons. The Drell-Yan reaction [2] on nuclear targets provides, in particular, the possibility of probing the propagation of projectile through nuclear matter, with the produced lepton pair carrying away the desired information on the projectile after it has travelled in the nucleus. Only initial-state interactions are important in Drell- Yan process since the dimuon in the final state does not interact strongly with the partons in the nuclei. This makes Drell-Yan scattering an ideal tool to study energy loss [3]. Drell-Yan scattering is closely related to deep-inelastic scattering (DIS) of leptons,but unlike DIS,it is directly sensitive to antiquark contributions in target parton distributions. When DIS on nuclei occurs at x < 0.08, where x is the parton momentum fraction, the cross section per nucleon decreases with increasing nucleon number A due to shadowing [4]. Shadowing should also occur in Drell-Yan dimuon production at small x 2, the momentum fraction of the target parton, and theoretical calculations indicate that shadowing in the two reactions has a common [5] origin. The energy loss effect is another nuclear effect apart from the nuclear effect on the parton distribution as in DIS scattering process. Shadowing and initial state energy loss effect are processes that occur in both Drell-Yan reaction and J/ψ formation.characterizing the energy loss effect in nuclear matter should further the understanding of J/ψ production,which is required if it is to be used as a signal for the quark-gluon plasma in relativistic heavy ion collisions. In 1999, Fermilab Experiment866(E866) [6] reported the precise measurement of the ratios of the Drell-Yan cross section per nucleon for an 800GeV proton beam incident on Be, Fe and W target at larger values of x 1,the momentum fraction of the beam parton, larger values of x F ( x 1 x 2 ),and smaller values of x 2 2

3 than reached by the previous experiment, Fermilab E772 [7]. The extended kinematic coverage of E866 significantly increases its sensitivity to energy loss and shadowing. Recently, M.B.Johnson et al. [8] and Francois Arleo [9] gave theoretical analysis of the E866 Drell-Yan experimental data by means of different methods, respectively.johnson et al. examined the effect of initial state energy loss on the Drell-Yan cross section ratios versus the incident proton s momentum fraction by employing a new formulation of the Drell-Yan process in the rest frame of nucleus. Francois Arleo carried out a leading-order analysis of E866 Drell-Yan data in nuclei according to multiple scattering of a high energy parton traversing a large nucleus ( cold QCD matter) studied by Baier et al. [10],in which the multiple soft gluon emission from the incoming parton leads to the parton energy loss. Since the EMC effect was discovered, various phenomenological models have been proposed to investigate the nuclear effect [11,12,13,14].Bickerstaff et al. [15] found that although most of the theoretical models provide goodexplanations for the EMC effect,they do not give a good description of the nuclear Drell-Yan process. Most of them overestimate the Drell-Yan different cross section ratios.in previous paper [16],we suggested an additional nuclear effect due to the energy loss in nuclear Drell-Yan process by means of the Glauber model [17],which have been extensively employed in nucleus-nucleus reaction with good fit to related experiment [18].It was found that the nuclear Drell-Yan ratio is suppressed significantly as a consequence of continuous energy loss of the projection proton to the target nucleon in their successive binary nucleon-nucleon collisions. This suppression balances the overestimate of the Drell-Yan ratio only by consideration of the nuclear effect from the parton distribution. 3

4 Recently,there were two trials to obtain nuclear parton distributions from the existing world experimental data. In 1999,K.J.Eskola et al.(eks) [19] suggested a set of nuclear parton distributions,which are studied within a framework of the DGLAP evolution.the measurements of F A 2 /FD 2 in deep inelastic la collisions, and Drell-Yan dilepton cross sections measured in pa collisions were used as constraints.the kinematical ranges are 10 6 x 1 and 2.25GeV 2 Q GeV 2 for nuclei from deuteron to heavy ones.with the nuclear parton distributions, the calculated results agreed very well with the relative EMC and Fermilab E772 experimental data. In 2001,M.Hirai et al.(hkm) [20] proposed two types of nuclear parton distributions which were obtained by quadratic and cubic type analysis.,and determined by a χ 2 global analysis of existing experimental data on nuclear structure functions without including the proton-nucleus Drell-Yan process.the kinematical ranges covered 10 9 x 1 and 1GeV 2 Q GeV 2 for nuclei from deuteron to heavy ones. As a result, they obtained reasonable fit to the measured experimental data of F 2. In this report, by means of the EKS and HKM nuclear parton distribution functions,the Drell-Yan production cross section rations for 800Gev proton incident on a variety of nuclear targets are analyzed by using the Glauber model with taking into account of the energy loss of the projective proton through nuclei. II Method According to Glauber model [17], the projectile proton scattering inelastically on nucleus (A) makes many collisions with nucleons bound in nuclei.the probability of having n collisions at an impact parameter b can be expressed as P( b,n) = A! n!(a n)! [T( b)σ in ] n [1 T( b)σ in ] A n, (1) where σ in ( 30mb)is non-diffractive cross section for inelastic nucleon-nucleon col- 4

5 lision,and T( b) is the thickness function of impact parameter b. For collisions of nucleons which are not polarized, the collisions does not depend on the orientation of b, and T( b) depends only on the magnitude b = b. So, we could consider only this case of T( b) = T(b). In an nucleon-nucleus collision without impact parameter selection, the number of nucleon-nucleon collisions n (for n = 1 to A) has a probability distribution P(n) = d bp(n, b). (2) A d bp(n, b) n=1 In following calculation, the thickness function can be conveniently written as [18] T( b) = 3 2πR 3 A 1 2πβAexp( b 2 /2βA), 2 A 32, 2 RA 2 b 2 θ(r A b ), A > 32. Here R A = r 0 A 1/3 is the radius of a colliding nucleus with r 0 = 1.2fm, θ is a step function, and β A = 0.606A 1/3. In multiple-collision Glauber model, the basic process is nucleon-nucleon collision for proton-nucleus Drell-Yan process.the leading-order contribution to the Drell-Yan process is quark-antiquark annihilation into a lepton pair. The annihilationcrosssection canbeobtainedfromthee + e µ + µ crosssectionbyincluding (3) the color factor 1 3 with the charge e2 f for the quark of flavor f. dˆσ dm = 8πα2 9M e2 fδ(ŝ M 2 ), (4) where ŝ = x 1 x 2 s,is the center of mass system (c.m.system) energy of q q collision,x 1 (resp.x 2 )is the momentum fraction carried by the projectile (resp.target)parton, s is the center of mass energy of the hadronic collision, and M is the invariant mass of the produced dimuon. The hadronic Drell-Yan differential cross section is then obtained from the convolution of the above partonic cross section with the 5

6 quark distributions in the beam and in the target hardron: d 2 σ dx 1 dm = 1 K8πα2 e 2 9M x 1 s f[q p f (x 1) q f A (x 2 )+ q p f (x 1)qf A (x 2 )], (5) f where K is the high-order QCD correction, α is the fine-structure constant, and q p(a) f f (x) and q p(a) (x) are the quark and anti-quark distributions in the proton (nucleon in the nucleus A).In addition,one has the kinematic relations, with the Feynman scaling variable x 1 x 2 = M2 s,x F = x 1 x 2, (6) x F = 2p l s, (7) where p l is the longitudinal momentum of the virtual photon, Now let us take into account of the energy loss of the projectile proton moving through nuclei. In proton-nucleus Drell-Yan collision, the incident proton passes through the nucleus befor producing the high Q 2 dimuon pair. On the one hand,the projectile proton may interact spectator nucleon bound in nuclei,in which soft (nonperturbative) minimum bias collisions may occur before making the final lepton pair.as a result,the projectile proton imparts energy to the struck nucleon and therefore must loose energy. On the other hand, the projectile proton, which travels through nucleus with existence of multiple-collisions, may emit soft gluon between two bias collisions in the nucleus,and must consequently experience an energy loss. Thus the energy loss from two above aspects in multiple collisions can induce the decrease of c.m.system energy of the nucleon-nucleon collision producing dimuon,and affect the measured Drell-Yan cross section. After the projectile proton has n collisions with nucleons in nuclei, suppose for conveniently calculation that the c.m.system energy of the nucleon-nucleon collision producing dimuon can 6

7 be expressed as s = s (n 1) s, (8) where s is the c.m.system energy loss per collision in the initial state. Therefore, the cross section for Drell-Yan process can be rewritten as d 2 σ (n) dx 1 dm = K8πα2 9M 1 x 1 s Here the rescaled quantities are defined as f e 2 f [qp f (x 1 ) qa f (x 2 )+ qp f (x 1 )qa f (x 2 )]. (9) x 1,2 = r sx 1,2, (10) with the c.m.system energy ratio: r s = s s, (11) because of x F = 2p l s = r s x F. (12) It is obvious that r s is always greater than one. Combining above ingredients, The measured Drell-Yan cross section in proton-nucleus collision experiments can be expressed as III Results and Discussion d2 σ dx 1 M = A n=1 P(n) d2 σ (n) dx 1 M, (13) InordertocomparewiththeexperimentaldatafromE866collaboration [6],we introduce the nuclear Drell-Yan ratios as: R A1 /A 2 (x 1 ) = dm d 2 σ p A 1 dx 1 dm (14) dm d 2 σ p A 2 dx 1. dm The integral range on M is determined according to the E866 experimental kinematic region.in our theoretical analysis,χ 2 is calculated with the Drell-Yan differ- 7

8 ential cross section rations R A1 /A 2 as χ 2 = j (R data A 1 /A 2,j Rtheo A 1 /A 2,j )2 (R err A 1 /A 2,j )2, (15) wheretheexperimental errorisgivenbysystematic errorsasr err A 1 /A 2,j, andrdata A 1 /A 2,j ( R theo A 1 /A 2,j ) indicates the experimental data (theoretical values ) for the ratior A 1 /A 2. IftheEKS [19] nuclear partondistributionfunctionsareused togetherwith CTEQ (the coordinated Theoretical Experimental Project on QCD ) [21] parton distribution functions in proton,obtained χ 2 value is χ 2 = 51.4 without energy loss effects for the 56 total data points. The χ 2 per degrees of freedom is given by χ 2 /d.o.f. = It is shown that theoretical results agree very well with the E866 experimental data,which results from EKS parametrization of nuclear parton distributions studied with including the Drell-Yan process. In addition,we consider also using HKM [20] nuclear parton distribution functions together with MRST [22] parton distribution functions in proton. The calculated results with HKM cubic type of nuclear parton distribution are shown in Fig.1 and Fig.2. which is the Drell-Yan cross section ratios for Fe to Be and W to Be as functions of x 1 for various interval of M,respectively.The solid curves are the ratios with only the nuclear effect on the parton distribution as in DIS scattering process, and the dotted curves correspond to an energy loss effect: s = 0.18GeV with nuclear effect on structure function. Obtained χ 2 values are χ 2 = with energy loss effect(i),χ 2 = (ii) without energy loss effect,respectly,for the 56 total data points. The χ 2 per degrees of freedom are χ 2 /d.o.f. = 1.007(i),2.567(ii),respectively. Employing the HKM quadratic type of nuclear parton distribution,χ 2 values are χ 2 = with energy loss effect,χ 2 = without energy loss effect,respectly.the χ 2 per degrees of freedom are χ 2 /d.o.f. = 1.015,2.569, respectively. This implies that the observed 8

9 energy loss of the incident proton is s = 0.18GeV at 1σ,which is almost equal to our previous results s = 0.2GeV [16]. From comparison with the experimental data, it is found that our theoretical results with energy loss effect are in good agreement with the Fermilab E866. In summary, we have made a leading-order analysis of E866 data in nuclei within the framework of the Glauber model by taking into account of the energy loss effect of the beam proton.in continuous multiple collisions,the energy loss effect in initial state causes the suppression of the proton-induced nuclear Drell-Yan cross section. It is found that the theoretical results with energy loss are in good agreement with the Fermilab E866 experiment by means of the parametrization of nuclear parton distributions studied without nuclear Drell-Yan process. This is another nuclear effect apart from the nuclear effect on the parton distribution as in DIS scattering process. The nuclear effect on structure functions and initial state energy loss can occur in both Drell-Yan production and J/ψ formation. Hence, these researches should also further the understanding of J/ψ production. Considering the existence of energy loss effect in Drell-Yan lepton pairs production,we think that the determination of nuclear parton distribution functions should not include Drell-Yan experimental data.although there are abundant data on electron and moun deep inelastic scattering, valence quark distributions in the small x region and the anti-quark distributions are difficultly determined.at this stage,only valence quark distributions in medium x region can be relatively well determined. It is well considered that the precise nuclear parton distributions must be known in order to calculate cross sections of high energy nuclear reactions accurately and find a signature of quark-gluon plasma in high energy heavy-ion reactions.we suggest precise neutrino scattering experiments,which can provide a good method 9

10 for measuring the F 2 (x,q 2 ) and xf 3 (x,q 2 ) structure functions.using the average of xf νa 3 (x,q 2 )and xf νa 3 (x,q 2 ), the valence quark distribution functions can be well determined. Combining the lepton inelastic scattering data with the neutrino scattering experiments, valence quark and anti-quark distribution functions will be obtained in the future,which makes us good understanding the energy loss effect in high energy nuclear Drell-Yan collisions. Acknowledgement:This work is partially supported by Major State Basic Research Development program (under Contract No. G ), by the National Natural Science Foundation of China(No , , ), and by Natural Science Foundation of Hebei Province(No ) References [1] W.Busza R Ledoux, Ann.Rev.Nucl.Part.Sci.,38(1989)119. [2] S.Drell and T.M.Yan, Phys.Rev,Lett.,25(1970)316. [3] G.T.Garvey and J.C.Peng,Phys.Rev.Lett.,90(2003) [4] M.Arneodo.et.al.(EMC), Nucl.Phys,B441(1995)3. [5] S.J.Brodsky,A.Hebecker,E.Quark.Phys.Rev.D.55.(1997)2584. [6] M.A.Vasiliev,et.al.(E866),Phys.Rev.Lett.83(1999)2304. [7] D.M.Adle et al.(e772),phys.rev.lett.,64(1990)2479 [8] M.B.Johnson,B.Z.Kopeliovich and I.K.Potashnikova,Phys.Rev.Lett.,86(2001)4483 [9] F.Arleo,Phys.Lett.,B532(2002)231 10

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12 Fig.1 The nuclear Drell-Yan cross section ratios R A1 /A 2 (x 1 ) on Fe to Be for various intervals M. Solid curves correspond to nuclear effect on structure function. Dotted curvesshowthecombinationofshadowing andenergylosseffect( s = 0.18GeV) with HKM cubic type of nuclear parton distributions.the experimental data are taken from the E866[6]. Fig.2 The nuclear Drell-Yan cross section ratios R A1 /A 2 (x 1 ) on W to Be for various intervals M. The comments are the same as Fig.1 12